Pseudo-Regularly Varying Functions and Generalized Renewal Processes (eBook)

Valerii Buldygin (1946–2012) received his PhD in Mathematics from Kiev Shevchenko University in 1973, and went on to work at the Institute of Mathematics, which is part of the Academy of Science of Ukraine (1973–1986) and at the National Technical University of Ukraine “Igor Sikorski Kyiv Polytechnic Institute” (1986–2012). His fields of research were probability and statistics with a special emphasis on limit theorems in Banach spaces, matrix normalizations in limit theorems, and asymptotic properties of correlograms and estimators of impulse transfer functions for linear systems. Karl-Heinz Indlekofer received his PhD in Mathematics from the Albert Ludwigs University of Freiburg im Breisgau in 1970. From 1970 to 1974 he worked at the Johann Wolfgang Goethe University of Frankfurt am Main. Since 1974 he has served as a Professor of Mathematics at the University of Paderborn. His field of research is analytic and probabilistic number theory with a special emphasis on sieve methods, limit theorems in number theory and arithmetical semigroups.Oleg I. Klesov received his PhD in Mathematics from Kiev Shevchenko University in 1981. He worked at the same University as a scientific researcher until 1990, when he moved to the National Technical University of Ukraine “Igor Sikorski Kyiv Polytechnic Institute”. His fields of research include probability and stochastic processes with a special emphasis on random fields, limit theorems in probability, and the reconstruction of stochastic processes from discrete observations.Josef G. Steinebach received his PhD in Mathematics from the University of Dusseldorf in 1976. After a visit to Carleton University, Ottawa, in 1980, he worked as a Professor of Mathematics at the Universities of Marburg (1980–1987, 1991–2002), Hannover (1987–1991), and Cologne (since 2002). His field of research is probability and statistics with a special emphasis on change-point analysis, limit theorems in probability, and asymptotic statistics.

Preface.- Equivalence of limit theorems for sums of random variables and renewal processes.- Almost sure convergence of renewal processes.- Generalizations of regularly varying functions.- Properties of absolutely continuous functions.- Non-degenerate groups of regular points.- Karamata’s theorem for integrals.- Asymptotically quasi-inverse functions.- Generalized renewal processes.- Asymptotic behavior of solutions of stochastic differential equations.- Asymptotics for renewal processes constructed from multi-indexed random walks.- Spitzer series and regularly varying functions. – Appendix: Some Auxiliary Results.- References.- Index.